3] CORRECTED ELEMENTS OF NEPTUNE. 55 



Hence we find, 



Inclination of the Orbit 146'49"'1+ 3' 7" 



Longitude of Descending Node 310 3' 44"'0 + 30' 37" 



Semi-latus Rectum 30'228 + 0'0922. 



Also, if e be the eccentricity of the orbit and a the true anomaly, 



ecosa= 0-00733 0-00235 

 esina= -0'06223 0'1167. 



Hence the most probable values of the eccentricity and longitude of the 

 perihelion appear to be, 



Eccentricity = 0'06266. 



Longitude of Perihelion = 49 58'. 



These latter are merely given as the results of the calculation, the 

 magnitude of the probable error of e sin a shewing that no weight is to 

 be attached to them. It may be seen, however, that the eccentricity cannot 

 be large. 



The most probable value of the mean distance = 30'35, with a probable 

 uncertainty of about 0"25 : the corresponding periodic time=167"2 sidereal 

 years, which is very nearly double that of Uranus. Hence the mutual dis- 

 turbances of these two planets will present some remarkable peculiarities 

 analogous to those of the first and second, and of the second and third 

 satellites of Jupiter. 



The probable errors given above have been found by considering the 

 probable error of each observation to be 3", the mean of the observations 

 on August 4 and August 12 (which, however, agree very well with each 

 other) being taken as a single observation. 



This estimation appears to be quite high enough, as the remaining 

 differences between theory and observation only exceed that amount in two 

 instances. 



